Have you ever been in a science laboratory? Take a look at this dilemma.

One of the places that the students were able to visit when they went downtown was a laboratory at the city college. Downtown, the city college had some of its classrooms and one of the classrooms was a laboratory.

“This is a good friend of mine Professor Smith,” Mr. Travis said introducing the students to a woman with blonde hair and a wide smile.

Many students responded yes and then were drawn over to one of the laboratory tables where a lot of work was taking place.

“What is happening here?” Sam asked.

“Well, I started with a very small sample of cobalt. I actually had 10 grams of it and I took a third of a third of a third of a third of it,” She explained.

The students began figuring the math out in their heads.

Can you figure it out? How many grams did the sample end up being? By the end of this Concept, you will be able to solve this dilemma.

Guidance

This may sound confusing, but in math, we can rewrite this as \begin{align*}\frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2}\end{align*}12⋅12⋅12⋅12 or \begin{align*}\left(\frac{1}{2} \right)^4\end{align*}(12)4. We can use exponents with fractions or quotients, too. In order to answer the question above, we would multiply the numerators and denominators across, like this: \begin{align*}\frac{1 \cdot 1 \cdot 1 \cdot 1}{2 \cdot 2 \cdot 2 \cdot 2}=\frac{1}{16}\end{align*}1⋅1⋅1⋅12⋅2⋅2⋅2=116. Half of a half of a half of a half is one sixteenth. Once again, we have repeating multiplication of the same number which we could write more easily as \begin{align*}\frac{1^4}{2^4}=\frac{1}{16}\end{align*}1424=116.

ThePower of a Quotient Propertysays that for any nonzero numbers \begin{align*}a\end{align*}a and \begin{align*}b\end{align*}b and any integer \begin{align*}n\end{align*}n: